Could you help giving me explanations on this problem ? Thank You !x

Let X be a normal random variable with unknown mean ,u and known variance 02 = 1. . The null hypothesis is that no = 2; . The alternative hypothesis is that m = 3. Let X1, . . . Xn be H = 20 independent samples of X , and let Z be Z := Zoning- : X1 + 2X2 3X3 + 4)::1 + (1)nan. i=1 (a) I I Compute the expectation and variance of Z. (b) __ F4 Let C be the critical region C := {(X1,...,Xn) | Z 2 19}. Find the value It so that the type I error of this critical region is o: = 0.05. (e) (5 points) Compute the type II error for the test in part (b)